Additionally to curvature and roughness preservation metrics, we also calculated the structural similarity score between the two point clouds, that has shown to highly correlate with the human perception [1]}. In particular, the Point-Cloud Structural Distortion Measure (SDM) can be defined as:
\(D(\mathcal {P}_1, \mathcal {P}_2) = \frac{\alpha \mathcal {L}(p_i, \hat{p}_i)+\beta \mathcal {C}(p_i, \hat{p}_i) +\gamma \mathcal {S}(p_i, \hat{p}_i)}{\alpha + \beta + \gamma }\) 
\(\mathcal {L}(p_i, \hat{p}_i) = \frac{||\bar{\mathcal {K}_1}(p_i) -\bar{\mathcal {K}_2}(\hat{p}_i) ||}{\max ( \bar{\mathcal {K}_1}(p_i),\bar{\mathcal {K}_2}(\hat{p}_i))}\) 
\(\mathcal {C}(p_i, \hat{p}_i)= \frac{||\sigma _{\bar{\mathcal {K}_1}}(p_i) -\sigma _{\bar{\mathcal {K}_2}}(\hat{p}_i) ||}{\max ( \bar{\mathcal {K}_1}(p_i),\bar{\mathcal {K}_2}(\hat{p}_i))}\) 
\(\mathcal {S}(p_i, \hat{p}_i)= \frac{||\sigma _{\bar{\mathcal {K}_1}}(p_i)\sigma _{\bar{\mathcal {K}_2}}(\hat{p}_i) - \sigma _{\bar{\mathcal {K}}_{12}}(p_i,\hat{p}_i)^2 ||}{\sigma _{\bar{\mathcal {K}_1}}(p_i)\sigma _{\bar{\mathcal {K}_2}}(\hat{p}_i)}\) 
